Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1896246 | Journal of Geometry and Physics | 2012 | 18 Pages |
Abstract
On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Ampère operator is defined. It is shown that it satisfies a version of the theorems of A. D. Alexandrov and Chern–Levine–Nirenberg. For more special classes of manifolds analogous results were previously obtained in Alesker (2003) [1] for the flat quaternionic space HnHn and in Alesker and Verbitsky (2006) [5] for hypercomplex manifolds. One of the new technical aspects of the present paper is the systematic use of the Baston differential operators, for which we also prove a new multiplicativity property.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Semyon Alesker,